I bought my 1961 Shasta Airflyte with the intentions of towing it with my 1962 Impala SS. I have looked for an original hitch for my car and have had no luck. Did GM offer a hitch as an option or accessory? Maybe the hitches back then were custom made to fit a car by the trailer dealer?
Anyone towing with a vintage car? What did you do for a hitch setup?
Hitches for passenger cars were sold as dealer, not factory, options. Most of my experience is with Ford, but this likely had a GM part number, as opposed to aftermarket, although aftermarket kits certainly existed. This means that you'd either walk in to your Chevrolet dealer and say you wanted a hitch installed on your new Impala, or you'd walk up to their parts counter and ask for the kit, possibly installed by their service department, or get an aftermarket kit (sometimes the same part in a different box) from your trailer dealer.
Be aware that some of those old kits were pretty severely underengineered, and most would be lucky to stand up to class 1 standards. If you happen to find an old kit, I'd personally view it as more of a starting point than a bolt-on solution, but that's just me. I'd plan on some custom work from someone knowledgeable and experienced with hitch fabrication.
Draw tite was a major supplier of hitches back then for hitches up to 3500 pounds. Reece was probably the largest supplier of equalizing hitches. I would go to a shop specializing in truck and trailer equipment. You might try a U-haul store if you have one near you, another place to try might be a NAPA store they used to be able to special order hitches. Hope this helps if not you may have to get a universal kit and have it welded up. That is what I did for my 1941 Plymouth. Good Luck